IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v202y2013i1p161-18310.1007-s10479-011-0840-4.html
   My bibliography  Save this article

A matrix continued fraction approach to multiserver retrial queues

Author

Listed:
  • Tuan Phung-Duc
  • Hiroyuki Masuyama
  • Shoji Kasahara
  • Yutaka Takahashi

Abstract

We consider basic M/M/c/c (c≥1) retrial queues where the number of busy servers and that of customers in the orbit form a level-dependent quasi-birth-and-death (QBD) process with a special structure. Based on this structure and a matrix continued fraction approach, we develop an efficient algorithm to compute the joint stationary distribution of the numbers of busy servers and retrial customers. Through numerical experiments, we demonstrate that our algorithm works well even for M/M/c/c retrial queues with large value of c. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Tuan Phung-Duc & Hiroyuki Masuyama & Shoji Kasahara & Yutaka Takahashi, 2013. "A matrix continued fraction approach to multiserver retrial queues," Annals of Operations Research, Springer, vol. 202(1), pages 161-183, January.
    • Handle: RePEc:spr:annopr:v:202:y:2013:i:1:p:161-183:10.1007/s10479-011-0840-4
    DOI: 10.1007/s10479-011-0840-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-011-0840-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-011-0840-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ger Koole & Avishai Mandelbaum, 2002. "Queueing Models of Call Centers: An Introduction," Annals of Operations Research, Springer, vol. 113(1), pages 41-59, July.
    2. Bong Choi & Yong Chang & Bara Kim, 1999. "MAP 1 , MAP 2 /M/c retrial queue with guard channels and its application to cellular networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 231-248, December.
    3. A. Gómez-Corral, 2006. "A bibliographical guide to the analysis of retrial queues through matrix analytic techniques," Annals of Operations Research, Springer, vol. 141(1), pages 163-191, January.
    4. Vladimir Anisimov & Jesus Artalejo, 2002. "Approximation of multiserver retrial queues by means of generalized truncated models," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 51-66, June.
    5. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    6. J.R. Artalejo & M. Pozo, 2002. "Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue," Annals of Operations Research, Springer, vol. 116(1), pages 41-56, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alexander Moiseev & Anatoly Nazarov & Svetlana Paul, 2020. "Asymptotic Diffusion Analysis of Multi-Server Retrial Queue with Hyper-Exponential Service," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    2. Shin, Yang Woo, 2015. "Algorithmic approach to Markovian multi-server retrial queues with vacations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 287-297.
    3. Samira Taleb & Amar Aissani, 2016. "Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 291-317, December.
    4. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vyacheslav Abramov, 2006. "Analysis of multiserver retrial queueing system: A martingale approach and an algorithm of solution," Annals of Operations Research, Springer, vol. 141(1), pages 19-50, January.
    2. B. Krishna Kumar & R. Sankar & R. Navaneetha Krishnan & R. Rukmani, 2022. "Performance Analysis of Multi-processor Two-Stage Tandem Call Center Retrial Queues with Non-Reliable Processors," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 95-142, March.
    3. Benjamin Legros & Sihan Ding & Rob Mei & Oualid Jouini, 2017. "Call centers with a postponed callback offer," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1097-1125, October.
    4. Mehmet Tolga Cezik & Pierre L'Ecuyer, 2008. "Staffing Multiskill Call Centers via Linear Programming and Simulation," Management Science, INFORMS, vol. 54(2), pages 310-323, February.
    5. Reynold E. Byers & Kut C. So, 2007. "Note--A Mathematical Model for Evaluating Cross-Sales Policies in Telephone Service Centers," Manufacturing & Service Operations Management, INFORMS, vol. 9(1), pages 1-8, January.
    6. Merve Bodur & James R. Luedtke, 2017. "Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty," Management Science, INFORMS, vol. 63(7), pages 2073-2091, July.
    7. Suri Gurumurthi & Saif Benjaafar, 2004. "Modeling and analysis of flexible queueing systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(5), pages 755-782, August.
    8. Barth, Wolfgang & Manitz, Michael & Stolletz, Raik, 2008. "Analysis of Two-Level Support Systems with Time-Dependent Overflow - A Banking Application," Hannover Economic Papers (HEP) dp-399, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    9. Artalejo, J.R. & Economou, A. & Lopez-Herrero, M.J., 2007. "Algorithmic approximations for the busy period distribution of the M/M/c retrial queue," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1687-1702, February.
    10. Kawai, Yosuke & Takagi, Hideaki, 2015. "Fluid approximation analysis of a call center model with time-varying arrivals and after-call work," Operations Research Perspectives, Elsevier, vol. 2(C), pages 81-96.
    11. Sofiane Ouazine & Karim Abbas, 2016. "A functional approximation for retrial queues with two way communication," Annals of Operations Research, Springer, vol. 247(1), pages 211-227, December.
    12. Vijay Mehrotra & Thomas A. Grossman, 2009. "OR Process Skills Transform an Out-of-Control Call Center into a Strategic Asset," Interfaces, INFORMS, vol. 39(4), pages 346-352, August.
    13. Bernd Heidergott & Arie Hordijk & Nicole Leder, 2010. "Series Expansions for Continuous-Time Markov Processes," Operations Research, INFORMS, vol. 58(3), pages 756-767, June.
    14. Athanassios N. Avramidis & Alexandre Deslauriers & Pierre L'Ecuyer, 2004. "Modeling Daily Arrivals to a Telephone Call Center," Management Science, INFORMS, vol. 50(7), pages 896-908, July.
    15. Lyes Ikhlef & Ouiza Lekadir & Djamil Aïssani, 2016. "MRSPN analysis of Semi-Markovian finite source retrial queues," Annals of Operations Research, Springer, vol. 247(1), pages 141-167, December.
    16. Sandjai Bhulai & Taoying Farenhorst-Yuan & Bernd Heidergott & Dinard Laan, 2012. "Optimal balanced control for call centers," Annals of Operations Research, Springer, vol. 201(1), pages 39-62, December.
    17. Elvin Coban & Aliza Heching & Alan Scheller‐Wolf, 2019. "Service Center Staffing with Cross‐Trained Agents and Heterogeneous Customers," Production and Operations Management, Production and Operations Management Society, vol. 28(4), pages 788-809, April.
    18. Avramidis, Athanassios N. & Chan, Wyean & Gendreau, Michel & L'Ecuyer, Pierre & Pisacane, Ornella, 2010. "Optimizing daily agent scheduling in a multiskill call center," European Journal of Operational Research, Elsevier, vol. 200(3), pages 822-832, February.
    19. Anatoly Nazarov & Alexander Moiseev & Svetlana Moiseeva, 2021. "Mathematical Model of Call Center in the Form of Multi-Server Queueing System," Mathematics, MDPI, vol. 9(22), pages 1-13, November.
    20. Hyun-Soo Ahn & Rhonda Righter & J. Shanthikumar, 2005. "Staffing decisions for heterogeneous workers with turnover," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 499-514, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:202:y:2013:i:1:p:161-183:10.1007/s10479-011-0840-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.